The potential influences of digitization on the mental health of personnel in the healthcare sector are increasingly coming into the scientific focus in the healthcare sector, especially in terms of the use of information and communication technologies. To date, there have been no German studies of the effects of technostress in healthcare. This cross-sectional study examined the relationships between technostress, burnout, work engagement, and job satisfaction among physicians in the field of urology. Data were collected via an online survey based on the job demands–resources model and the concept of technostress. The survey was sent to German urologists working in inpatient clinics. The participating physicians experienced moderate levels of technostress (M = 2.67, SD = 0.69). The results, based on a general linear model analysis, showed that technostress is significantly positively associated with burnout (β = 0.293; p < 0.001) and negatively associated with work engagement (β = −0.175; p < 0.001) and job satisfaction (β = −0.206; p < 0.001). This study also identified stress and strain factors associated with the use of ICT and assessed institutional support offers as coping mechanisms. The results of this study and its formulated practical implications can serve as a basis for discussing sustainable digitalization strategies in hospitals, taking into consideration technostress and its impact on physicians’ burnout, work engagement and job satisfaction.